Method for predicting water content of closed cycle drying system product based on Bagging dual integration strategy

Abstract

The invention discloses a method for predicting the water content of a product in a closed-loop drying system based on a Bagging dual integration strategy, which comprises the following steps of: collecting data of the closed-loop drying system, normalizing the data, keeping original data, and correspondingly dividing the data before and after processing into a training set, a verification set and a test set; selecting an improved artificial neural network as a base learner, and training based on a Bagging dual integration strategy to generate a plurality of sub-models; and screening the sub-models by using a multi-target particle swarm optimization algorithm, selecting high-quality sub-models according to accuracy and diversity, carrying out simple average combination, selecting proper model parameters, and finally obtaining a Bagging-based dual integration model. A comparison result shows that the method provided by the invention has better performance in the aspects of accuracy and robustness, and can be used for predicting the water content of the product in the industrial drying process.

Description

Technical Field

[0001] The present invention belongs to the field of drying of chemical products, and particularly relates to a method for predicting the water content of products in a closed-loop circulation drying system based on a Bagging double integration strategy. Background Art

[0002] Drying is widely used in industries such as chemical engineering, pharmaceuticals, agriculture, and biomass processing. Traditional drying has problems such as high energy consumption, low efficiency, and large pollution. As a new type of high-efficiency and energy-saving drying technology, the closed-loop circulation drying system can effectively improve energy efficiency and reduce pollution, and is suitable for complex industrial drying processes. However, the closed-loop circulation drying process involves the properties of multiple physical fields and multi-scale heat transfer / mass transfer, as well as the characteristics of drying medium circulation and energy integration, which bring many challenges to industrial applications.

[0003] In recent years, with the development of computer science, machine learning has played a crucial role in modeling, prediction, control, and solving complex process problems. As a heuristic machine learning method, the artificial neural network (ANN) can handle processes with defined ambiguity, nonlinearity, and complexity, and has low model development costs and is beneficial for optimization, providing an effective alternative for modeling complex drying processes. However, ANN usually relies on a large amount of data for training. Actual industrial data often has problems such as incompleteness or anomalies, and its performance will be limited. Moreover, due to the data-oriented nature of ANN, the prediction results lack physical consistency.

[0004] Ensemble learning can effectively improve the prediction accuracy and generalization ability of the model by combining the prediction results of multiple models. Bagging is a popular ensemble learning method that creates diverse base learners by adjusting the random distribution of the training data set, thereby reducing variance and eliminating overfitting. As the number of base learners increases, the computational cost and bias will gradually increase, and the interpretability of the model will decrease. Snapshot ensemble is an ensemble method that does not require additional training costs, that is, multiple snapshot models are saved by periodically adjusting the learning rate during a single training process, avoiding the problem of training multiple models from scratch. Since these snapshots are saved from the same training process under the same data distribution, they often have similarities and may produce the same prediction results. Therefore, the advantages of the two ensemble models can be combined to further improve the performance of the model. Summary of the Invention

[0005] In order to accurately monitor the water content of products during the drying process, with the aim of improving product quality and optimizing process parameters, the present invention provides a method for predicting the water content of products in a closed-loop drying system based on the Bagging double integration strategy. Specifically, it is a method for predicting the water content of a closed-loop drying system that uses an improved artificial neural network as the base learner and integrates the results of multiple base learners using the Bagging double integration strategy. This effectively alleviates the physical inconsistency of the prediction results, improves the prediction accuracy, generalization ability, and stability of the model, and ensures the reliability and accuracy of the model results in a changing production environment.

[0006] A method for predicting the water content of products in a closed-loop drying system based on the Bagging double integration strategy includes the following steps:

[0007] Step 1: Use a closed-loop drying system to dry wet materials to obtain dried products. Collect the data of the drying system and perform normalization processing on the data to obtain the processed data. Corresponding divide the data before and after processing into a training set, a validation set, and a test set;

[0008] Step 2: Construct an improved artificial neural network as the base learner in the integrated training;

[0009] Step 3: Input the training set data into the base learner and generate multiple sub-models according to the Bagging double integration strategy for training;

[0010] Step 4: Use the validation set data to verify the quality of the sub-models, and use the multi-objective particle swarm optimization algorithm to screen the sub-models according to accuracy and diversity;

[0011] Step 5: After screening the obtained sub-models, perform integration in a simple average combination manner to construct a Bagging double integration model;

[0012] Step 6: Use the Bagging double integration model to predict the water content of the products in the dryer;

[0013] In Step 1, the drying system data includes:

[0014] The inlet air temperature, water content, and flow rate of the rotary flash dryer;

[0015] The outlet air temperature, water content, material temperature, and water content of the rotary flash dryer;

[0016] The inlet circulating air temperature, water content, and flow rate of the fluidized bed dryer;

[0017] The outlet air temperature, water content, material temperature, and water content of the fluidized bed dryer.

[0018] In Step 1, the normalization process uses the following formula:

[0019]

[0020] where x new is the normalized feature variable, x is the feature variable in the original data, and x min is the minimum value in the original data, and x max is the maximum value in the original data.

[0021] In Step 1, the data before and after processing is correspondingly partitioned. 60% of the data is used as the training set, 20% of the data is used as the validation set, and 20% of the data is used as the test set.

[0022] In Step 2, an improved artificial neural network is constructed, specifically including: the output of the simplified drying physical model is used as the auxiliary feature of the neural network, the neural network learns the prediction residuals of the physical model, and a loss function introducing physical constraints. The total loss function Loss total has the following formula:

[0023] Loss total =(1 - λ)Loss train +λLoss PHY (2)

[0024]

[0025] where n is the number of samples, Loss train is the supervised loss function between the true value and the predicted value, Y is the true value, is the predicted value, Loss PHY represents the physical loss function, is the outlet material temperature, is the predicted value of the outlet material temperature, and λ is the physical loss weight.

[0026] In Step 3, multiple sub-models are generated according to the Bagging double integration strategy. The specific steps are as follows: randomly sample the training set using Bootstrap, repeat the sampling K times to obtain K independent training sets, and use the snapshot integration technique to save M snapshot models on each training set, resulting in a total of K×M sub-models.

[0027] In Step 4, the definitions of accuracy and diversity are as follows:

[0028] Definition 1 (Accuracy) Evaluate the errors of all candidate sub-models using the validation set, and the overall prediction accuracy index RMSE avg is:

[0029]

[0030] Among them, RMSE m represents the root mean square error of the m-th sub-model, n is the number of validation samples, and y val,i is the true value on the i-th validation sample, is the predicted value of the m-th sub-model on the i-th validation sample, and m T is the number of screened models.

[0031] Definition 2 (Diversity) uses the correlation coefficient to measure the diversity between sub-models. The greater the difference between two sub-models, the smaller the error correlation coefficient of their predicted outputs. The correlation coefficient between any two sub-models is:

[0032]

[0033] Among them, r is the correlation coefficient, e i , e j are the predicted output errors of any two sub-models respectively, Cov() is the covariance, and Var() is the variance operator. The average value of the correlation coefficients between sub-models is used as the diversity index r avg , and the formula is as follows:

[0034]

[0035] In step 5, the simple average combination is defined as:

[0036]

[0037] Among them, y pred is the predicted value based on the Bagging double integration model, is the predicted value of the i-th sub-model.

[0038] The technical solution of the present invention is as follows:

[0039] Step 1: Use a closed-circuit drying system to dry the wet material to obtain a dried product, collect the drying system data, perform normalization processing on the data to obtain the processed data. Corresponding the data before and after processing into a training set, a validation set, and a test set;

[0040] Step 2: Construct an improved artificial neural network as the base learner in the integrated training;

[0041] Step 3: Input the training set data into the base learner and generate multiple sub-models according to the Bagging double integration strategy for training;

[0042] Step 4: Use the validation set data to verify the quality of the sub-models, and use the multi-objective particle swarm optimization algorithm to screen the sub-models according to accuracy and diversity;

[0043] Step 5: The sub-models obtained through screening are integrated in a simple average combination method to construct a Bagging double integration model.

[0044] Step 6: Use the test set data to perform performance testing on the Bagging double integration model.

[0045] In Step 1, the data collected from the closed-loop circulation drying system specifically includes: the inlet air temperature, moisture content, and flow rate of the rotary flash dryer; the outlet air temperature, moisture content, material temperature, and moisture content of the rotary flash dryer; the inlet circulating air temperature, moisture content, and flow rate of the fluidized bed dryer; the outlet air temperature, moisture content, material temperature, and moisture content of the fluidized bed dryer. Since the sizes and orders of magnitude of the data are different (such as temperature, moisture content, and flow rate), directly using the original operating condition data for modeling will amplify the error. Therefore, the data is normalized according to Equation (1) to eliminate the order of magnitude influence, ensure the comparability between different variables, and retain the original information to the greatest extent.

[0046]

[0047] where, x new is the normalized characteristic variable, x is the characteristic variable in the original data, x min is the minimum value in the original data, and x max is the maximum value in the original data.

[0048] Since the output of the physical model needs to be used as an auxiliary characteristic variable in the subsequent steps, and the law of conservation of mass and the law of conservation of energy are used as physical constraints, it is necessary to save the original data and make it correspond to the normalized data.

[0049] In Step 2, an improved artificial neural network is constructed as the base learner in the integrated training.

[0050] The architecture of the improved artificial neural network is as follows:

[0051] Take the output of the simplified drying physical model as the auxiliary feature of the neural network, that is, f NN (X, Y PHY ), where X represents the characteristic variable and Y PHY is the output of the physical model;

[0052] The neural network learns the prediction residuals of the physical model, that is

[0053] Introduce the loss function with physical constraints, that is, Loss total =(1 - λ)Loss train + λLossPHY , where Loss total is the total loss function, Loss train is the supervised loss function, Loss PHY is the physical loss function, and λ is the physical loss weight.

[0054] The output of the improved artificial neural network is: where is the residual value predicted by the neural network.

[0055] Simplified drying physical model: Taking the wet material and the drying medium (air) as the objects, the overall mass and energy balances of the drying process are carried out, and the moisture content model of the dried product is constructed. The specific calculation process is as follows.

[0056] Law of conservation of mass:

[0057] W = L1(H3 - H1) + L2(H3 - H2) = G c (MC1 - MC2) (2)

[0058] where, W is the change in moisture content in the wet material, kg / h; G c is the mass flow rate of the dry material, kg / h; MC1 and MC2 are the initial and final moisture contents of the wet material, kg / kg; L1 is the mass flow rate of dry air at the inlet of the rotary flash dryer, kg / h; H1 is the moisture content of the air at the outlet of the rotary flash dryer, kg / kg; L2 and H2 are the mass flow rate of dry air and the moisture content, kg / h and kg / kg, respectively, from the fin heat exchanger to the inlet of the fluidized bed dryer; H3 is the moisture content of the air at the outlet of the fluidized bed dryer, kg / kg.

[0059] Law of conservation of energy:

[0060] L1I1 + L2I2 + G c I′1 = (L1 + L2)I3 + G c I′2 (3)

[0061] where, I1, I2 and I3 are the enthalpy values of the air from the outlet of the rotary flash dryer to the inlet of the fluidized bed dryer, from the outlet of the fin heat exchanger to the inlet of the fluidized bed dryer, and the outlet of the fluidized bed dryer, kJ / kg; I′1 and I′2 are the enthalpy values of the material at the inlet and outlet of the fluidized bed dryer, kJ / kg.

[0062]

[0063] G c (I′2 - I′1) = G c (c s2 + c w2 MC2)(θ2 - θ1) - Wcw1 θ1 (6)where, and is the specific heat capacity of the air entering the fluidized bed dryer and the circulating air, kJ / (kg·℃); c s2 is the specific heat capacity of dry material, kJ / (kg·℃); c w2 is the specific heat capacity of water, kJ / (kg·℃); c v1 is the specific heat capacity of water vapor, kJ / (kg·℃); r0 is the latent heat of vaporization of water, kJ / kg; t1 is the outlet air temperature of the rotary flash dryer, ℃; t2 is the inlet air temperature from the finned heat exchanger to the fluidized bed dryer, ℃; t3 is the outlet air temperature of the fluidized bed dryer, ℃; θ1 is the inlet material temperature from the rotary flash dryer to the fluidized bed dryer, ℃; θ2 is the outlet material temperature of the fluidized bed dryer, ℃.

[0064] The simplified drying physical model (product moisture content) expression is obtained by combining the mass and energy conservation laws:

[0065]

[0066] Among them, c s is the specific heat capacity of dry material, kJ / (kg·℃); c w is the specific heat capacity of water, kJ / (kg·℃); c v is the specific heat capacity of water vapor, kJ / (kg·℃); c H is the specific heat capacity of moist air, kJ / (kg·℃).

[0067] Physical loss function: The temperature loss value is incorporated into the neural network as a physical constraint, so that the network considers the impact of temperature changes on humidity during training. The temperature and physical loss function formulas are as follows:

[0068]

[0069] The total loss function is as follows:

[0070] Loss total =(1-λ)Loss train +λLoss PHY (10)

[0071]

[0072] Among them, n is the number of samples, Loss train is the supervised loss function between the true value and the predicted value, Y is the true value, is the predicted value, Loss PHY represents the physical loss function, is the outlet material temperature, The predicted value of the outlet material temperature, λ is the physical loss weight.

[0073] In step 3, training is performed using the bagging dual ensemble strategy to generate multiple sub-models. Specifically, this involves randomly sampling the training set using bootstrap, repeating the sampling K times to obtain K independent training sets. Then, using snapshot ensemble technology, M snapshot models are saved on each training set, resulting in a total of K × M sub-models.

[0074] Snapshot integration periodically adjusts the learning rate so that the model converges to multiple local minimum points and escapes during the optimization process, saving the model parameters derived from these different local minima. The formula for the cyclic cosine annealing learning rate α(t) is:

[0075]

[0076] Where α0 is the initial learning rate, t is the number of iterations, T is the total number of training iterations, and M is the number of cycles. Snapshot ensemble divides the entire training process into M cycles, with each cycle having T / M iterations.

[0077] In step 4, the definitions of accuracy and diversity are given below.

[0078] Definition 1 (Accuracy) uses the validation set to evaluate the error of all candidate sub-models, and the overall prediction accuracy indicator RMSE avg for:

[0079]

[0080] Among them, RMSE m represents the root mean square error of the mth sub-model, n is the number of validation samples, y val,i is the true value on the i-th validation sample, is the predicted value of the mth sub-model on the i-th validation sample, m T is the number of screening models.

[0081] Definition 2 (Diversity) uses the correlation coefficient to measure the diversity between sub-models. The greater the difference between two sub-models, the smaller the error correlation coefficient of their prediction output. The correlation coefficient between any two sub-models is:

[0082]

[0083] Among them, r is the correlation coefficient, e i ,e j The prediction output errors of any two sub-models are respectively, Cov() is the covariance, Var() is the variance operator. The average value of the correlation coefficient between the sub-models is used as the diversity index r avg, The formula is as follows:

[0084]

[0085] In step 5, the simple average combination is defined as:

[0086]

[0087] where y pred is the predicted value based on the Bagging double integration model, is the predicted value of the i-th sub-model.

[0088] In step 6, the test set is used to test the performance of the Bagging double integration model saved in step 5, and the mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), and coefficient of determination (R 2 ) are used as evaluation indicators for the model performance.

[0089] Compared with the prior art, the present invention has the following advantages:

[0090] A method for predicting the water content of a product in a closed-loop drying system based on a Bagging double integration strategy proposed by the present invention. The main advantages are the integration of physics, knowledge, and data, modifying the architecture of the artificial neural network, training based on the Bagging double integration strategy, and using a multi-objective particle swarm optimization algorithm for integration pruning. This method enhances the ability of the network model to extract and utilize the data set, and makes the information learned by the network more in line with physical laws, generating models with high prediction accuracy and diversity based on the double integration strategy. Compared with other methods, this method has higher prediction accuracy and robustness, and has certain application prospects in the same industrial system. Description of the Drawings

[0091] The drawings are used to provide further understanding of the present invention, and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the present invention, and do not constitute a limitation to the present invention. In the drawings:

[0092] Figure 1 is the process flow diagram of the closed-loop drying system, including a dehumidification tower T101, finned tube heat exchangers E101 and E103, a plate heat exchanger E102, an air filter V101, a rotary flash dryer D101, and a fluidized bed dryer D102.

[0093] Figure 2 is the improved architecture diagram of the artificial neural network.

[0094] Figure 3 is the flow chart of the Bagging double integration model.

[0095] Figure 4 Scatter plots between the predicted values and the true values of different models, where, (A) - Improved artificial neural network (ENN), (B) - Bagging ensemble model (Bagging), (C) - Snapshot ensemble model (Snapshot), (D)

[0096] - Bagging double ensemble model (SnapBag). Specific embodiments

[0097] The following will combine the accompanying drawings and embodiments to detail the implementation manner of the present invention, so as to fully understand how the present invention applies technical means to solve technical problems and achieve the implementation process of technical effects and implement accordingly.

[0098] The improved artificial neural network architecture diagram of the present invention is as Figure 2 shown, and improvements are made to the input, output, and loss function parts of the artificial neural network model. Specifically, in the input part of the artificial neural network, the output Y PHY (i.e., the moisture content MC2 predicted based on the physical model) is introduced as an auxiliary feature and input into the network together with the feature variable X. Since the neural network predicts the residual based on the drying physical model therefore Y is added to its output part PHY to obtain the final predicted output The overall loss function Loss of the neural network total consists of two parts: the supervised loss function Loss train , and the physical loss function Loss PHY .

[0099] The schematic diagram of the method of the Bagging double ensemble model of the present invention is as Figure 3 shown. Based on the improved artificial neural network, the Bagging ensemble strategy, the Snapshot ensemble strategy, and the multi-objective particle swarm optimization algorithm are combined. Specifically, the Bagging ensemble strategy is used to adjust the random distribution of the training data to generate multiple training subsets, and each base model is independently trained based on the improved artificial neural network algorithm. During the training process, the Snapshot strategy is used to generate multiple snapshot base models again. Then, the multi-objective particle swarm optimization algorithm is used to screen and optimize these snapshot base models, and finally a highly accurate and diverse ensemble model is obtained.

[0100] This model is used in a glyphosate drying system that combines a rotary flash dryer and a fluidized bed dryer, and its process is as Figure 1As shown in the figure. The main equipment includes a screw feeder, a dehumidification tower T101, finned heat exchangers E101 and E103, a plate heat exchanger E102, an air filter V101, a rotary flash dryer D101, and a fluidized bed dryer D102. The brief technological process is as follows: The wet material is continuously fed into the rotary flash dryer by the screw feeder, dispersed by the rotary agitator at the bottom and heated by the high-speed hot circulating gas introduced, and after most of the moisture is removed, it is discharged from the top with the air flow and further dried in the fluidized bed dryer with an internal cloth bag until the product moisture content requirement is met. The tail gas from the fluidized bed dryer is divided into two paths. One part enters the rotary flash dryer after being filtered, dust-removed, pressurized, and heated; the other part enters the fluidized bed dryer after being dust-removed, pressurized, condensed, and dehumidified.

[0101] Step 1, the data collected from the closed-loop circulation drying system specifically includes: the inlet air temperature, moisture content, and flow rate of the rotary flash dryer; the outlet air temperature, moisture content, material temperature, and moisture content of the rotary flash dryer; the inlet circulating air temperature, moisture content, and flow rate of the fluidized bed dryer; the outlet air temperature, moisture content, material temperature, and moisture content of the fluidized bed dryer. Since the sizes and orders of magnitude of the data are different (such as temperature, moisture content, and flow rate), directly using the original operating condition data for modeling will amplify the error. The data is normalized to eliminate the influence of the order of magnitude, ensure the comparability between different variables, and retain the original information to the greatest extent.

[0102] In order to train, evaluate, and verify the performance and generalization ability of the model, the data before and after processing is correspondingly divided. 60% of the data is used as the training set, 20% of the data is used as the validation set, and 20% of the data is used as the test set.

[0103] Step 2, construct an improved artificial neural network and use it as the base learner in the ensemble training. The base learner is the basic unit of the ensemble model, and each base learner is independently trained in the ensemble.

[0104] The architecture of the improved artificial neural network is as follows: (1) Use the output of the simplified drying physical model as the auxiliary feature of the neural network, that is, f NN (X, Y PHY ), where X represents the feature variable and Y PHY is the output of the physical model; (2) The neural network learns the prediction residuals of the physical model, that is, (3) Introduce a loss function with physical constraints, that is, Loss total =(1 - λ)Loss train +λLoss PHY , where Loss total is the total loss function, Loss train is the supervised loss function, Loss PHYis the physical loss function, and λ is the physical loss weight.

[0105] The output of the improved artificial neural network is:

[0106] The simplified drying physical model refers to the product moisture content equation solved by combining the mass and energy balance laws in the drying system. The specific process is as follows:

[0107] Law of Conservation of Mass:

[0108] W=L1(H3-H1)+L2(H3-H2)=G c (MC1-MC2) (1)

[0109] Where W is the change in moisture in the wet material, kg / h; G c is the mass flow rate of dry material, kg / h; MC1 and MC2 are the initial and final moisture contents of wet material, kg / kg; L1 is the mass flow rate of dry air at the inlet of the rotary flash dryer, kg / h; H1 is the moisture content of the air at the outlet of the rotary flash dryer, kg / kg; L2 and H2 are the mass flow rate and moisture content of dry air from the fin heat exchanger to the inlet of the fluidized bed dryer, kg / h and kg / kg, respectively; H3 is the moisture content of the air at the outlet of the fluidized bed dryer, kg / kg.

[0110] The law of conservation of energy:

[0111] L1I1+L2I2+G c I′1=(L1+L2)I3+G c I′2 (2)

[0112] Among them, I1, I2 and I3 are the air enthalpy values from the outlet of the rotary flash dryer to the inlet of the fluidized bed dryer, from the outlet of the fin heat exchanger to the inlet of the fluidized bed dryer, and the outlet of the fluidized bed dryer, respectively, in kJ / kg; I′1 and I′2 are the material enthalpy values at the inlet and outlet of the fluidized bed dryer, respectively, in kJ / kg.

[0113]

[0114] G c (I′2-I′1)=G c (c s2 +c w2 MC2)(θ2-θ1)-Wc w1 θ1 (5)

[0115] Among them, c H1 and is the specific heat capacity of the air entering the fluidized bed dryer and the circulating air, kJ / (kg·℃); c s2is the specific heat capacity of dry material, kJ / (kg·℃); c w2 is the specific heat capacity of water, kJ / (kg·℃); c v1 is the specific heat capacity of water vapor, kJ / (kg·℃); r0 is the latent heat of vaporization of water, kJ / kg; t1 is the outlet air temperature of the rotary flash dryer, ℃; t2 is the inlet air temperature from the finned heat exchanger to the fluidized bed dryer, ℃; t3 is the outlet air temperature of the fluidized bed dryer, ℃; θ1 is the inlet material temperature from the rotary flash dryer to the fluidized bed dryer, ℃; θ2 is the outlet material temperature of the fluidized bed dryer, ℃.

[0116] Combining the mass and energy conservation laws gives the expression for the product moisture content:

[0117]

[0118] where c s is the specific heat capacity of dry material, kJ / (kg·℃); c e is the specific heat capacity of water, kJ / (kg·℃); c v is the specific heat capacity of water vapor, kJ / (kg·℃); c H is the specific heat capacity of humid air, kJ / (kg·℃).

[0119] Among them, the physical loss function takes the temperature loss value as a physical constraint and incorporates it into the neural network, enabling the network to consider the influence of temperature changes on humidity during training. The temperature and physical loss function formulas are as follows:

[0120]

[0121] The total loss function is as follows:

[0122] Loss total =(1 - λ)Loss train +λLoss PHY (9)

[0123]

[0124] where n is the number of samples, Loss train is the supervised loss function between the true value and the predicted value, Y is the true value, is the predicted value, Loss PHY represents the loss function extracted from the physical laws, is the outlet material temperature, the predicted value of the outlet material temperature, and λ is the physical loss weight.

[0125] Improved artificial neural network training process: (1) The data X representing the characteristic variables is input into the simplified drying physical model to obtain the physical output YPHY , namely the auxiliary variable; (2) Input the feature variable and the auxiliary variable into the neural network architecture, and the neural network learns the prediction residuals of the physical model. The mapping relationship between the input and the output is (3) The final output of the improved neural network is The improved neural network has six fully connected layers, which successively contain 14 / 9 / 12 / 10 / 7 / 1 neurons; (5) Evaluate the model performance by setting different λ values. When λ = 0.2, the model performance is the best.

[0126] Step 3: Construct a Bagging double integration strategy (SnapBag) for predicting the water content of products in a closed-loop drying system. The Bagging double integration strategy is divided into two parts: the integration model and the integration pruning.

[0127] The first part: Use Bootstrap to randomly sample the training set and repeat the sampling K times to obtain K independent training sets. On each training set, use the snapshot integration technology to train the base learner, and save M snapshot models during the training process. A total of K×M sub-models are obtained in the integration model stage.

[0128] The snapshot integration adjusts the learning rate periodically, so that the model converges to multiple local minimum points and escapes during the optimization process, and saves the model parameters derived from these different local minimum points. The cyclic cosine annealing learning rate formula is:

[0129]

[0130] Among them, α0 is the initial learning rate, t is the number of iterations, T is the total number of training iterations, and M is the number of cycle periods. The snapshot integration divides the entire training process into M periods, and the number of iterations in each period is T / M.

[0131] The second part: Use the multi-objective particle swarm optimization algorithm for the K×M sub-models obtained in the first part, and screen them according to accuracy and diversity, and eliminate the sub-models with poor performance and high similarity.

[0132] Definition 1 (Accuracy) Use the validation set to evaluate the errors of all candidate sub-models, and the overall prediction accuracy index RMSE avg is:

[0133]

[0134] Among them, RMSE m represents the root mean square error of the m-th sub-model, n is the number of validation samples, y val,i is the true value on the i-th validation sample, is the predicted value of the m-th sub-model on the i-th validation sample, m Tis the number of screening models.

[0135] Definition 2 (Diversity) uses the correlation coefficient to measure the diversity between sub-models. The greater the difference between two sub-models, the smaller the error correlation coefficient of their predicted outputs. The correlation coefficient between any two sub-models is:

[0136]

[0137] where r is the correlation coefficient, e i , e j are the predicted output errors of any two sub-models respectively, Cov() is the covariance, and Var() is the variance operator. The average value of the correlation coefficients between sub-models is used as the diversity index r avg , and the formula is as follows:

[0138]

[0139] When designing and optimizing the double integration strategy, the following three key parameters are selected: the initial learning rate α0, the number of cycles M, and the number of integrated sub-models m T . Through experiments, it can be seen that when α0 = 0.01, M = 3, and m T = 10, the model performance is better.

[0140] Table 1 Influence of different learning rates on the SnapBag model

[0141]

[0142] Table 2 Influence of different numbers of cycles on the SnapBag model

[0143]

[0144] Table 3 Influence of different numbers of integrated sub-models on the SnapBag model

[0145]

[0146] Step 4, compare the model performance of the double integration model based on Bagging (SnapBag) with the improved artificial neural network (ENN), Bagging, and snapshot integration (Snapshot). It can be seen from Table 4 that SnapBag has a higher R 2 value and lower prediction error. To intuitively reflect the difference in model accuracy, Figure 4 a scatter plot of the predicted values and true values of different models is shown. The model prediction accuracy can be judged from the degree of aggregation of the scatter plot. The symbols of the SnapBag model are more concentrated on the 1:1 line, while the symbols of the other three models are more dispersed.

[0147] Performance Comparison of Different Models

[0148]

Claims

1. A method for predicting the water content of products in a closed-loop drying system based on a Bagging double integration strategy, comprising the following steps: Step 1: Use a closed-loop drying system to dry wet materials to obtain dried products, collect drying system data as the data before processing, perform normalization processing on the data to obtain the processed data, and correspondingly divide the data before and after processing into a training set, a validation set, and a test set; Step 2: Construct an improved artificial neural network as the base learner in the integrated training; Step 3: Input the data of the training set into the base learner, and generate multiple sub-models according to the Bagging double integration strategy for training; Step 4: Use the data of the validation set to verify the quality of the sub-models, and use the multi-objective particle swarm optimization algorithm to screen the sub-models according to accuracy and diversity; Step 5: After screening the obtained sub-models, perform integration in a simple average combination manner to construct a Bagging double integration model; Step 6: Use the Bagging double integration model to predict the water content of the products in the dryer.

2. The method for predicting the water content of the product of the closed-loop circulation drying system based on the Bagging double integration strategy according to claim 1, wherein, In Step 1, the drying system data includes: The inlet air temperature, water content, and flow rate of the rotary flash dryer; The outlet air temperature, water content, material temperature, and water content of the rotary flash dryer; The inlet circulating air temperature, water content, and flow rate of the fluidized bed dryer; The outlet air temperature, water content, material temperature, and water content of the fluidized bed dryer.

3. The method for predicting the moisture content of the product of the closed-loop circulation drying system based on the Bagging double integration strategy according to claim 1, wherein In Step 1, the normalization processing uses the following formula: where x new is the normalized feature variable, x is the feature variable in the original data, x min is the minimum value in the original data, x max is the maximum value in the original data.

4. The method for predicting the moisture content of the product of the closed-loop circulation drying system based on the Bagging double integration strategy according to claim 1, wherein, In Step 1, correspondingly dividing the data before and after processing into a training set, a validation set, and a test set specifically includes: Correspondingly divide the data before and after processing, 55 - 65% of the data as the training set, 15 - 25% of the data as the validation set, and 15 - 25% of the data as the test set.

5. The method for predicting the water content of the product of the closed-loop circulation drying system based on the Bagging double integration strategy according to claim 1, wherein In Step 2, constructing an improved artificial neural network as the base learner in the integrated training specifically includes: The output of the dry physical model serves as an auxiliary feature for the neural network. The neural network learns the prediction residuals of the physical model and introduces a loss function with physical constraints, and the total loss function is Loss total The formula is as follows: Loss total =(1 - λ)Loss train + λLoss PHY (2) where n is the number of samples, Loss train is the supervision loss function between the true value and the predicted value, Y is the true value, is the predicted value, Loss PHY represents the loss function extracted from physical laws, is the outlet material temperature, is the predicted value of the outlet material temperature, and λ is the physical loss weight.

6. The method for predicting the moisture content of the product of the closed-loop circulation drying system based on the Bagging double integration strategy according to claim 1, wherein In Step 3, the specific steps of generating multiple sub-models according to the Bagging double integration strategy: Use Bootstrap to randomly sample the training set, repeat the sampling K times to obtain K independent training sets, use the snapshot integration technology, and save M snapshot models on each training set, resulting in a total of k×M sub-models.

7. The method for predicting the moisture content of the product of the closed-loop circulation drying system based on the Bagging double integration strategy according to claim 1, characterized in that In Step 4, the multi-objective particle swarm optimization algorithm is to simulate the behavior of a particle swarm in the search space, use the concepts of non-dominated sorting and Pareto optimal solutions to find a balance between multiple objectives, and gradually optimize the objective function by updating the positions and velocities of the particles.

8. The method for predicting the water content of the product of the closed-loop circulation drying system based on the Bagging double integration strategy according to claim 1, wherein, In step 4, the accuracy evaluates the errors of all candidate sub-models using the validation set The overall accuracy is: Among them, RMSE avg is the accuracy. RMSE m represents the root mean square error of the m-th sub-model, n is the number of validation samples, y val,i is the true value on the i-th validation sample, is the predicted value of the m-th sub-model on the i-th validation sample, m T is the number of screened models; Diversity uses the correlation coefficient to measure the diversity between sub-models. The greater the difference between two sub-models, the smaller the correlation of the prediction errors. The correlation calculation formula is as follows: Among them, e i , e j are the prediction output errors of any two sub-models respectively, Cov() is the covariance, Var() is the variance operator, and after obtaining the correlation value, it is averaged as the overall diversity index r avg , and the formula is as follows:

9. The method for predicting the water content of the product of the closed-loop circulation drying system based on the Bagging double integration strategy according to claim 1, wherein, In Step 5, the simple average combination is defined as: Among them, y pred is the predicted value based on the Bagging double integration model, which is the predicted value of the sub-model.

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